There's simply too many humans for that any more, anyway. People leaving cities en masse would just be a large-mammal version of a locust swarm, or army/soldier ants on the move. They might devour everything they can get their hands on, yeah - and then have to resort to eating each other once all the wildlife and cattle is dead or run away.

You know that Simpsons halloween episode with the clone Homers devouring everything in their path? It'd be remarkably like that, but with more blood and swearing, and with millions and not "just a handful".

And as far as raiding fields goes ... some clowns were up to that around here a few years ago; they trampled more than they stole.